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Optimizing Multi-stage Production for an Assembly-Type Supply Chain with Unequal Sized Batch Shipments

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Abstract

This paper studies the multi-stage logistics and inventory problem in an assembly-type supply chain where a uniform lot size is produced uninterruptedly with a single setup at each stage. Partial lots, or sub-batches, can be transported to next stage upon completion. Unequal sub-batch sizes at each stage follow geometric series and the numbers of sub-batches across stages are allowed to be different. Since the mainline and each branch line of an assembly-type supply chain are series-type supply chains, a model of the series-type supply chain is first established and a model of the assembly-type supply chain is subsequently developed. Optimization algorithms that determine the economic lot sizes, the optimal sub-batch sizes and the number of sub-batches for each stage are developed. The polynomial-time algorithms incorporate the optimality properties derived in the paper to find the lower and upper bounds of the solutions by constructing the solution ranges and then the optimal solutions accordingly.

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Abbreviations

Q :

lot size,

X :

X={S,M,Bj}, where S,M,Bj denote SSC, mainline of ASC, and the jth branch line of ASC, respectively,

m Xi :

number of sub-batches at stage i in X,

q i(min) :

the minimal sub-batch size at stage i in SSC,

D :

constant product demand rate at the end stage of supply chain (units per unit time),

N X :

number of stages in X,

P Xi :

constant production rate at stage i in X (units per unit time),

h Xi :

inventory holding cost of stage i in X ($ per unit per unit time),

S Xi :

setup cost of stage i in X ($ per setup),

F Xi :

fixed transportation cost between stages i and (i+1) in X ($ per sub-batch),

[P Xi ]+ :

the greater production rate of stages i and (i+1) in X, or max(P Xi ,P X(i+1)),

[P Xi ]− :

the smaller production rate of stages i and (i+1) in X, or min(P Xi ,P X(i+1)),

[R Xi ]:

production rate ratio of stages i and (i+1) in X, i.e., [P Xi ]+/[P Xi ]−,

\(Q_{i,m_{Xi}}^{S}\) :

the critical lot size with m Xi sub-batches at stage i in X, where between stages i and (i+1) in X, there exists a critical lot size \(Q_{i,m_{Xi}}^{S}\) such that

S :

ordered critical lot size vector,

Nc :

number of elements in ordered critical lot size vector S,

RG i :

the range of the ith lot size,

M i :

the corresponding sub-batch vector of RG i .

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Authors and Affiliations

  1. Department of Business Administration, Takming University of Science and Technology, 56, Huan-Shan Rd., Section 1, Taipei, 11451, Taiwan, ROC

    Wen-Tsung Ho & Jason Chao-Hsien Pan

  2. Department of Logistics, Takming University of Science and Technology, 56, Huan-Shan Rd., Section 1, Taipei, 11451, Taiwan, ROC

    Yu-Cheng Hsiao

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  1. Wen-Tsung Ho
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  2. Jason Chao-Hsien Pan
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Correspondence to Wen-Tsung Ho.

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Communicated by Panos M. Pardalos.

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Ho, WT., Pan, J.CH. & Hsiao, YC. Optimizing Multi-stage Production for an Assembly-Type Supply Chain with Unequal Sized Batch Shipments. J Optim Theory Appl 153, 513–531 (2012). https://doi.org/10.1007/s10957-011-9951-y

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